Group #14565696 — subgroups

Subgroups — #14565696

Order 2432.

158 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597284	C₂	1	1	yes	maximal, characteristic
3	#11926927	C₂	1	1	yes	maximal, characteristic
4	#11926638	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926347	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#357	C₂	1	1	yes	maximal, characteristic
8	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
9	#10597382	—	2	1	no	—
10	C₂×#64526	—	2	1	no	—
11	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
12	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
13	#10597333	—	2	1	no	—
14	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#107	C₂²	1	1	yes	characteristic
16	#10597284	—	2	2	no	—
17	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
19	#10597267	—	2	1	no	—
20	Dic₁₅₂	—	2	2	no	—
21	C₂×D₄×C₁₉	—	2	1	no	—
22	C₂×Dic₃₈	—	2	1	no	—
23	C₂×Dic₃₈	—	2	1	no	—
24	D₈×C₁₉	—	2	1	no	—
25	D₈×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂²⋊Dic₁₉	—	4	1	no	—
29	C₂²⋊Dic₁₉	—	4	1	no	—
30	#64526	—	4	2	no	—
31	Dic₁₉⋊C₄	—	4	1	no	—
32	C₄×Dic₁₉	—	4	1	no	—
33	C₄×Dic₁₉	D₄	1	1	yes	characteristic
34	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
35	Dic₇₆	—	2	1	no	—
36	Dic₇₆	—	2	1	no	—
37	Dic₇₆	—	2	1	no	—
38	Dic₇₆	D₄	1	2	yes	—
39	C₁₆×C₁₉	—	2	1	no	—
40	C₁₉⋊C₁₆	—	2	1	no	—
41	C₂³×C₁₉	—	4	1	no	—
42	D₄×C₁₉	—	4	1	no	—
43	D₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×Dic₁₉	—	4	1	no	—
47	C₂×Dic₁₉	—	4	1	no	—
48	C₂×Dic₁₉	D₈	1	1	yes	characteristic
49	C₂×Dic₁₉	D₈	1	1	yes	characteristic
50	Dic₃₈	—	2	2	no	—
51	Dic₃₈	—	4	1	no	—
52	Dic₃₈	—	4	1	no	—
53	Dic₃₈	—	4	1	no	—
54	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₈×C₁₉	#41	1	1	yes	characteristic
56	C₁₉⋊C₈	—	2	1	no	—
57	#2211	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	—	8	1	no	—
59	C₂²×C₁₉	—	8	1	no	—
60	C₂²×C₁₉	—	8	1	no	—
61	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
62	C₄×C₁₉	—	8	1	no	—
63	C₄×C₁₉	#121	1	1	yes	characteristic
64	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
65	Dic₁₉	—	2	1	no	—
66	Dic₁₉	—	2	1	no	—
67	Dic₁₉	—	4	2	no	—
68	Dic₁₉	—	8	1	no	—
69	C₂×Q₃₂	—	19	1	no	—
70	C₂×SD₃₂	—	19	1	no	—
71	#495	—	19	1	no	—
72	C₄×Q₁₆	—	19	1	no	—
73	C₄⋊C₁₆	—	19	1	no	—
74	#358	—	19	1	no	—
75	#357	D₁₉	1	1	yes	characteristic
76	C₂×C₁₉	—	16	1	no	—
77	C₂×C₁₉	#459	1	1	yes	characteristic
78	C₂×C₁₉	#508	1	1	yes	characteristic
79	C₂×C₁₉	#510	1	1	yes	characteristic
80	C₂×Q₁₆	—	19	1	no	—
81	C₂×Q₁₆	—	19	1	no	—
82	C₂×SD₁₆	—	38	1	no	—
83	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
84	#124	—	38	1	no	—
85	C₄×Q₈	—	38	1	no	—
86	Q₃₂	—	38	2	no	—
87	SD₃₂	—	38	2	no	—
88	C₂×C₁₆	—	19	1	no	—
89	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
90	#107	C₂×D₁₉	1	1	yes	characteristic
91	#103	—	38	1	no	—
92	C₄×C₈	—	19	1	no	—
93	C₁₉	#2211	1	1	yes	characteristic, complemented, Sylow
94	C₂×Q₈	—	38	1	no	—
95	C₂×Q₈	—	38	1	no	—
96	C₂×D₄	—	2	1	no	—
97	Q₁₆	—	19	2	no	—
98	Q₁₆	—	38	1	no	—
99	Q₁₆	—	38	1	no	—
100	Q₁₆	—	38	1	no	—
101	SD₁₆	—	76	2	no	—
102	D₈	—	2	1	no	—
103	D₈	—	2	1	no	—
104	C₂×C₈	—	19	1	no	—
105	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	76	1	no	—
108	C₂²⋊C₄	—	76	1	no	—
109	C₂²⋊C₄	—	76	1	no	—
110	C₄²	—	19	1	no	—
111	C₄²	—	76	1	no	—
112	C₁₆	—	2	1	no	—
113	C₁₆	—	38	1	no	—
114	C₂³	—	4	1	no	—
115	Q₈	—	38	2	no	—
116	Q₈	—	76	1	no	—
117	Q₈	—	76	1	no	—
118	Q₈	—	76	1	no	—
119	D₄	—	4	1	no	—
120	D₄	—	4	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	19	1	no	—
123	C₂×C₄	—	19	1	no	—
124	C₂×C₄	—	76	1	no	—
125	C₂×C₄	—	76	1	no	—
126	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
127	C₈	—	38	1	no	—
128	C₈	#64541	1	1	yes	characteristic
129	C₈	D₄×D₁₉	1	1	yes	characteristic
130	C₂²	—	8	1	no	—
131	C₂²	—	8	1	no	—
132	C₂²	—	8	1	no	—
133	C₂²	D₈×D₁₉	1	1	yes	characteristic
134	C₄	—	8	1	no	—
135	C₄	—	38	1	no	—
136	C₄	—	38	1	no	—
137	C₄	—	76	2	no	—
138	C₄	—	152	1	no	—
139	C₄	#10597330	1	1	yes	characteristic
140	C₄	#10597360	1	1	yes	characteristic
141	C₂	—	16	1	no	—
142	C₂	#11926738	1	1	yes	characteristic
143	C₂	#11926973	1	1	yes	characteristic
144	C₂	#11926983	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₁₅₂

C₂

yes

maximal, characteristic, complemented

C₂×#10597284

C₂

yes

maximal, characteristic

#11926927

C₂

yes

maximal, characteristic

#11926638

C₂

yes

maximal, characteristic, complemented

Dic₁₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#11926347

C₂

yes

maximal, characteristic, complemented

C₁₉×#357

C₂

yes

maximal, characteristic

C₂×D₈×C₁₉

C₂²

yes

characteristic

#10597382

—

C₂×#64526

—

C₂×Dic₇₆

C₂²

yes

characteristic

C₂×Dic₇₆

C₂²

yes

characteristic

#10597333

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

#10597284

—

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

#10597267

—

Dic₁₅₂

—

C₂×D₄×C₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

#64526

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Dic₇₆

—

Dic₇₆

—

Dic₇₆

—

Dic₇₆

D₄

yes

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

characteristic

C₂×Dic₁₉

D₈

yes

characteristic

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

#2211

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×Q₃₂

—

C₂×SD₃₂

—

#495

—

C₄×Q₁₆

—

C₄⋊C₁₆

—

#358

—

#357

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

C₂×D₁₉

yes

characteristic

#124

—

C₄×Q₈

—

Q₃₂

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

#107

C₂×D₁₉

yes

characteristic

#103

—

C₄×C₈

—

C₁₉

#2211

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

100

Q₁₆

—

101

SD₁₆

—

102

D₈

—

103

D₈

—

104

C₂×C₈

—

105

C₂×C₈

C₂²×D₁₉

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₁₆

—

113

C₁₆

—

114

C₂³

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

119

D₄

—

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

D₄×D₁₉

yes

characteristic

127

C₈

—

128

C₈

#64541

yes

characteristic

129

C₈

D₄×D₁₉

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

D₈×D₁₉

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

152

—

139

C₄

#10597330

yes

characteristic

140

C₄

#10597360

yes

characteristic

141

C₂

—

142

C₂

#11926738

yes

characteristic

143

C₂

#11926973

yes

characteristic

144

C₂

#11926983

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#357	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂×D₈×C₁₉	C₂²
hypercenter	#357	D₁₉
hypocenter	C₁₉	#2211
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#357

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂×D₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×Dic₁₅₂	C₂	semidirect
4. #11926638	C₂	semidirect
5. Dic₁₉⋊C₁₆	C₂	semidirect
6. #11926347	C₂	semidirect
93. C₁₉	#2211	semidirect

H ≅ G/N

type

1. C₂×Dic₁₅₂

C₂

semidirect

4. #11926638

C₂

semidirect

5. Dic₁₉⋊C₁₆

C₂

semidirect

6. #11926347

C₂

semidirect

93. C₁₉

#2211

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×Dic₁₅₂	2
C₂×#10597284	2
#11926927	2
#11926638	2
Dic₁₉⋊C₁₆	2
#11926347	2
C₁₉×#357	2
#2211	19

subgroup

index

C₂×Dic₁₅₂

Dic₁₉⋊C₁₆

C₁₉×#357

Subgroups — #14565696

Conjugacy classes of subgroups

Complements

Maximal subgroups